Details

sample99.0ms

Algorithm

intervals

Results

50.0ms	158×	body	1280	valid
22.0ms	26×	body	2560	valid
10.0ms	47×	body	640	valid
5.0ms	14×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	4×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
3.1b	(cos (+ x eps))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `cos-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

15.0ms	(- (cos (+ x eps)) (cos x))
10.0ms	(cos (+ x eps))

series64.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

simplify73.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	192	385
1	523	285
2	2519	275
3	5001	220

prune108.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(fma (sin x) (sin eps) (cos x))
1.9b	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `prod-diff` `log1p-expm1-u`
2×	`fma-udef`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `cos-mult` `*-commutative` `flip--` `cbrt-unprod` `associate--r+` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

10.0ms	(* (cos x) (cos eps))
0.0ms	(fma (sin x) (sin eps) (cos x))
12.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

series206.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* (cos x) (cos eps))
47.0ms	(fma (sin x) (sin eps) (cos x))
121.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

simplify117.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	235	486
1	832	409
2	4494	406
3	5001	404

prune209.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
1.9b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`prod-diff` `add-log-exp`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `fma-neg` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `associate--l+` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 93

Calls

4 calls:

10.0ms	(* (cos x) (cos eps))
17.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
11.0ms	(* (sin x) (sin eps))
66.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series278.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (cos x) (cos eps))
78.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
41.0ms	(* (sin x) (sin eps))
123.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify49.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	381	988
1	1342	837
2	5002	822

prune318.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.8b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (cos x) (cos eps) (- (* (sin eps) (sin x))))
0.2b	(* (sin eps) (sin x))
1.9b	(+ (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (- (* (sin x) (+ (- (sin eps)) (sin eps))) (cos x)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-log-exp`
7×	`add-cube-cbrt` `associate-+r+`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`expm1-log1p-u` `fma-def` `associate-r` `associate-l` `prod-diff` `log1p-expm1-u`
2×	`associate--l+` `sum-log` `fma-udef`
1×	`+-commutative` `distribute-rgt-in` `associate-+r-` `sub-neg` `associate-+l+` `distribute-lft-in` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `distribute-lft-out` `unswap-sqr`

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma (cos x) (cos eps) (- (* (sin eps) (sin x))))
14.0ms	(* (sin eps) (sin x))
43.0ms	(+ (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (- (* (sin x) (+ (- (sin eps)) (sin eps))) (cos x)))

series242.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(fma (cos x) (cos eps) (- (* (sin eps) (sin x))))
46.0ms	(* (sin eps) (sin x))
122.0ms	(+ (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (- (* (sin x) (+ (- (sin eps)) (sin eps))) (cos x)))

simplify37.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	280	733
1	981	671
2	5001	608

prune223.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.8b

regimes181.0ms

Accuracy

84.1% (1.6b remaining)

Error of 15.8b against oracle of 14.2b and baseline of 24.2b

bsearch125.0ms

Steps

Iters	Range		Point
11	4.083453529187016e-23	0.5429513389937057	9.805431973736002e-10
7	-1.5317450828987306e-09	-4.0039902443278174e-11	-1.3208939428373893e-09

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	22
1	56	22
2	58	22
3	58	22

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4474×	body	1280	valid
540.0ms	627×	body	2560	valid
390.0ms	1866×	body	640	valid
93.0ms	636×	body	320	valid
29.0ms	305×	body	160	valid
5.0ms	92×	body	80	valid